Problem: Simplify the following expression: $z = \dfrac{-6a^2 + 42a - 36}{a - 1} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-6$ , so we can rewrite the expression: $ z =\dfrac{-6(a^2 - 7a + 6)}{a - 1} $ Then we factor the remaining polynomial: $a^2 {-7}a + {6} $ ${-1} {-6} = {-7}$ ${-1} \times {-6} = {6}$ $ (a {-1}) (a {-6}) $ This gives us a factored expression: $\dfrac{-6(a {-1}) (a {-6})}{a - 1}$ We can divide the numerator and denominator by $(a + 1)$ on condition that $a \neq 1$ Therefore $z = -6(a - 6); a \neq 1$